Principles of Microeconomics

class: center, middle, inverse, title-slide

.title[
# Principles of Microeconomics
]
.author[
### ECO 2306
]
.date[
### <em>Fall 2022</em>
]

---

class: center, middle, inverse

# Chapter 11:
## Technology, Production, and Costs

---

## Introduction to Production Theory
.panelset[.panel[.panel-name[Technology]
- Analogous to Consumer Theory (Ch. 10)
- **Technology**
  - The basic activity of a firm is to use inputs to produce outputs of goods and services
  - Example inputs:
    - Workers,
    - Machines, and
    - Natural resources
- **Technological change**: 
  - A positive or negative change in the ability of a firm to produce a given level of output with a given quantity of inputs
  - **Positive technological change**: firm improves its ability to turn inputs into outputs
- This is a broad set of definitions. Some examples would include:
  - inventory control
  - the just-in-time system used by Toyota to reduce inventories of parts in its automobile assembly plants
]

.panel[.panel-name[Short- vs. Long-Run]
- **Short run**: the period of time during which at least one of a firm’s inputs is fixed
  - Example: A firm might have a long-term lease on a factory that is too costly to get out of
- In the **long run**, all costs are variable. That is a firm can:
  - vary all inputs, 
  -  adopt new technology, and 
  - increase or decrease the size of its physical plant
- How long is the long run? 
  - It varies from firm to firm.
  - Think of it as “a long enough period of time that anything can be changed.”
]
.panel[.panel-name[Fixed vs. Variable]
.pull-left[
- **Total cost** is the cost of all the inputs a firm uses in production
  - **Variable costs** are costs that change as output changes
  - **Fixed costs** are costs that remain constant as output changes
  - `$TC = FC + VC$`
]
.pull-right[
<table class="table table-striped table-hover table-condensed" style="font-size: 20px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Table: Fixed costs in the Publishing Industry</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> Cost </th>
   <th style="text-align:center;"> Amount </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> Salaries and benefits </td>
   <td style="text-align:center;"> $625,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Rent </td>
   <td style="text-align:center;"> $75,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Utilities </td>
   <td style="text-align:center;"> $20,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Supplies </td>
   <td style="text-align:center;"> $6,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Postage </td>
   <td style="text-align:center;"> $5,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Travel </td>
   <td style="text-align:center;"> $9,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Subscriptions, etc. </td>
   <td style="text-align:center;"> $5,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Miscellaneous </td>
   <td style="text-align:center;"> $5,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Total </td>
   <td style="text-align:center;"> $750,000 </td>
  </tr>
</tbody>
</table>
]
]
.panel[.panel-name[Implicit vs. Explicit]
.pull-left[
- Recall that economists like to consider all of the *opportunity costs* of an activity
- This includes both the explicit costs and the implicit costs
  - **Explicit cost**: A cost that involves spending money
  - **Implicit cost**: A non-monetary opportunity cost
- Suppose Jill Johnson quits her $30,000 a year job to start a pizza store. She uses $50,000 of her savings to buy equipment—furniture, etc.—and takes out a loan as well.
  - What are the explicit costs?
  - What are the implicit costs?
- All of these implicit costs are *real costs* of Jill owning the pizza store, even if they don’t require an explicit outlay of money.

]
.pull-right[
<table class="table table-striped table-hover table-condensed" style="font-size: 20px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Table: Example of Pizzaria Costs</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> Cost </th>
   <th style="text-align:center;"> Amount </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> Pizza dough, tomato sauce, etc. </td>
   <td style="text-align:center;"> $20,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Wages </td>
   <td style="text-align:center;"> $48,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Interest payments on loan to buy ovens </td>
   <td style="text-align:center;"> $10,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Electricity </td>
   <td style="text-align:center;"> $6,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Lease payment for store </td>
   <td style="text-align:center;"> $24,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Forgone salary </td>
   <td style="text-align:center;"> $30,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Forgone interest </td>
   <td style="text-align:center;"> $3,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Economic depreciation </td>
   <td style="text-align:center;"> $10,000 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Total </td>
   <td style="text-align:center;"> $151,000 </td>
  </tr>
</tbody>
</table>
]
]

]

---

## Short Run Production
.panelset[

.panel[.panel-name[Production Function]
- Goal: maximize profits
  - Profits = Total Revenue - Total Costs
  - Focus on reducing costs (producing as efficiently as possible)
- **Production function**: the relationship between the inputs employed and the maximum output it can produce with those inputs
- `$q = f(L, k)$`
  - q = quantity produced
  - L = labor (number of workers or number of hours worked)
  - k = capital
- Short-run: capital is fixed, `$q = f(L, \overline{k})$`
- Long-run: labor and capital are both variable
]

.panel[.panel-name[Discrete Production]
Jill is setting up her pizzaria with 2 pizza ovens. Each pizza oven costs $400 per week, and each worker costs $650 per week. Let's map out her production function.
<table class="table table-striped table-hover table-condensed" style="font-size: 18px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Table: Pizza Production</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> Workers </th>
   <th style="text-align:center;"> Ovens </th>
   <th style="text-align:center;"> Pizzas </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 200 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 450 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 550 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 600 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 625 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 640 </td>
  </tr>
</tbody>
</table>

]

.panel[.panel-name[MPL]
.pull-left[
**Marginal product of labor**: 
- the additional output a firm produces as a result of hiring one more worker
- `$MP_L = \frac{\Delta q }{\Delta L}$`

**Law of diminishing returns**: The principle that, at some point, adding more of a variable input, such as labor, to the same amount of a fixed input, such as capital, will cause the marginal product of the variable input to decline.
]
.pull-right[
<table class="table table-striped table-hover table-condensed" style="font-size: 18px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Table: Diminishing Marginal Products</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> Workers </th>
   <th style="text-align:center;"> Ovens </th>
   <th style="text-align:center;"> Pizzas </th>
   <th style="text-align:center;"> MPL </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> NA </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 200 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 450 </td>
   <td style="text-align:center;"> 250 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 550 </td>
   <td style="text-align:center;"> 100 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 600 </td>
   <td style="text-align:center;"> 50 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 625 </td>
   <td style="text-align:center;"> 25 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 640 </td>
   <td style="text-align:center;"> 15 </td>
  </tr>
</tbody>
</table>
]
]

.panel[.panel-name[MPL cont'd]
.pull-left[
<table class="table table-striped table-hover table-condensed" style="font-size: 18px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Table: Diminishing Marginal Products</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> Workers </th>
   <th style="text-align:center;"> Ovens </th>
   <th style="text-align:center;"> Pizzas </th>
   <th style="text-align:center;"> MPL </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> NA </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 200 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 450 </td>
   <td style="text-align:center;"> 250 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 550 </td>
   <td style="text-align:center;"> 100 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 600 </td>
   <td style="text-align:center;"> 50 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 625 </td>
   <td style="text-align:center;"> 25 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 640 </td>
   <td style="text-align:center;"> 15 </td>
  </tr>
</tbody>
</table>

]
.pull-right[
<div id="htmlwidget-e343fbfe7535a4dd23e6" style="width:100%;height:400px;" class="plotly html-widget"></div>
<script type="application/json" data-for="htmlwidget-e343fbfe7535a4dd23e6">{"x":{"data":[{"x":[0,1,2,3,4,5,6],"y":[0,200,450,550,600,625,640],"text":["Workers: 0<br />Pizzas:   0","Workers: 1<br />Pizzas: 200","Workers: 2<br />Pizzas: 450","Workers: 3<br />Pizzas: 550","Workers: 4<br />Pizzas: 600","Workers: 5<br />Pizzas: 625","Workers: 6<br />Pizzas: 640"],"type":"scatter","mode":"lines+markers","line":{"width":1.88976377952756,"color":"rgba(0,32,77,1)","dash":"solid"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","marker":{"autocolorscale":false,"color":"rgba(0,0,0,1)","opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(0,0,0,1)"}},"frame":null},{"x":[0,1,2,3,4,5,6],"y":[null,200,250,100,50,25,15],"text":["Workers: 0<br />MPL:  NA","Workers: 1<br />MPL: 200","Workers: 2<br />MPL: 250","Workers: 3<br />MPL: 100","Workers: 4<br />MPL:  50","Workers: 5<br />MPL:  25","Workers: 6<br />MPL:  15"],"type":"scatter","mode":"lines+markers","line":{"width":1.88976377952756,"color":"rgba(87,92,109,1)","dash":"dash"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","marker":{"autocolorscale":false,"color":"rgba(87,92,109,1)","opacity":1,"size":5.66929133858268,"symbol":"triangle-up-open","line":{"width":1.88976377952756,"color":"rgba(87,92,109,1)"}},"frame":null},{"visible":false,"showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","mode":"","frame":null}],"layout":{"margin":{"t":69.041095890411,"r":7.30593607305936,"b":65.4611872146119,"l":43.1050228310502},"plot_bgcolor":"rgba(235,235,235,1)","paper_bgcolor":"rgba(255,255,255,1)","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"title":{"text":"Products of Labor: Pizzaria's Output of Pizzas","font":{"color":"rgba(0,0,0,1)","family":"","size":17.5342465753425},"x":0,"xref":"paper"},"xaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[-0.3,6.3],"tickmode":"array","ticktext":["0","2","4","6"],"tickvals":[0,2,4,6],"categoryorder":"array","categoryarray":["0","2","4","6"],"nticks":null,"ticks":"outside","tickcolor":"rgba(51,51,51,1)","ticklen":3.65296803652968,"tickwidth":0.66417600664176,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(255,255,255,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"y","title":{"text":"Number of Workers per Week","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[-32,672],"tickmode":"array","ticktext":["0","200","400","600"],"tickvals":[0,200,400,600],"categoryorder":"array","categoryarray":["0","200","400","600"],"nticks":null,"ticks":"outside","tickcolor":"rgba(51,51,51,1)","ticklen":3.65296803652968,"tickwidth":0.66417600664176,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(255,255,255,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"x","title":{"text":"Pizzas per Week","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":null,"line":{"color":null,"width":0,"linetype":[]},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":false,"legend":{"bgcolor":"rgba(255,255,255,1)","bordercolor":"transparent","borderwidth":1.88976377952756,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.689497716895}},"hovermode":"closest","height":400,"barmode":"relative"},"config":{"doubleClick":"reset","modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"source":"A","attrs":{"21347ab8680e":{"x":{},"y":{},"type":"scatter"},"213458085226":{"x":{},"y":{}},"21346c69328f":{"x":{},"y":{}},"2134239578bb":{"x":{},"y":{}},"213454457b4c":{"x":{},"y":{}}},"cur_data":"21347ab8680e","visdat":{"21347ab8680e":["function (y) ","x"],"213458085226":["function (y) ","x"],"21346c69328f":["function (y) ","x"],"2134239578bb":["function (y) ","x"],"213454457b4c":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.2,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script>
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.panel[.panel-name[APL]
.pull-left[
- **Average product of labor**: total output produced by a firm divided by the quantity of workers
  - With 3 workers, the restaurant can produce 550 pizzas, giving an average product of labor of:
  - `$\frac{550}{3} = 183.3$`
  
- A useful way to think about this is that the **average product of labor** is the average of the marginal products of labor
  - The first three workers give 200, 250, and 100 additional pizzas respectively:
  - `$\frac{200+250+100}{3} = 183.3$`
]
.pull-right[
<table class="table table-striped table-hover table-condensed" style="font-size: 18px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Table: Diminishing Marginal Products</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> Workers </th>
   <th style="text-align:center;"> Ovens </th>
   <th style="text-align:center;"> Pizzas </th>
   <th style="text-align:center;"> MPL </th>
   <th style="text-align:center;"> APL </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> NA </td>
   <td style="text-align:center;"> NaN </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 200.0 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 450 </td>
   <td style="text-align:center;"> 250 </td>
   <td style="text-align:center;"> 225.0 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 550 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 183.3 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 600 </td>
   <td style="text-align:center;"> 50 </td>
   <td style="text-align:center;"> 150.0 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 625 </td>
   <td style="text-align:center;"> 25 </td>
   <td style="text-align:center;"> 125.0 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 640 </td>
   <td style="text-align:center;"> 15 </td>
   <td style="text-align:center;"> 106.7 </td>
  </tr>
</tbody>
</table>
]

]
.panel[.panel-name[MPL vs. APL]
.pull-left[
- So, the third worker made the average product of labor go down.

- This happened because the third worker produced less (marginal) output than the average of the previous workers.

1. When `$MP_L < AP_L$`, then `$AP_L$` is falling

2. When `$MP_L > AP_L$`, then `$AP_L$` is rising

3. When `$MP_L = AP_L$`, then `$AP_L$` is flat

College GPA example: your grade in one class (marginal value) brings up or down your GPA (average value) depending on whether the grade is more, less than or equal to your GPA value

]
.pull-right[
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]
]
]

---

## Long Run Production

.panelset[

.panel[.panel-name[Isoquants]
.pull-left[
- `$q = A*f(L, k)$`
- e.g.: `$q = \sqrt{L*k}$`
- All possible combinations of the two inputs needed to produce the same level of output
- Higher levels of output are represented by isoquant lines that are higher on the graph
- While we only show three isoquant lines there is a different one for every level of output
]
.pull-right[
<img src="data:image/png;base64,#images/mit_5_1.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[Corner cases]
.pull-left[
<img src="data:image/png;base64,#images/mit_5_2a.png" width="85%" style="display: block; margin: auto;" />
]
.pull-left[
<img src="data:image/png;base64,#images/mit_5_2b.png" width="90%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[MRTS]
.pull-left[
`$\text{Slope of isoquant} = \frac{\Delta k}{\Delta L}$`
  - the rate at which a firm will substitute one input for another while keeping output constant
  - This rate is called the **marginal rate of technical substitution (MRTS)** 
  - The next unit of labor times how productive that labor is needs to tradeoff equally with the next unit of capital times how productive that capital is
$$
`\begin{aligned}
\Delta L * MP_L + \Delta k * MP_k &= 0\\
\Delta L * MP_L &= -\Delta k * MP_k\\
MRTS = -\frac{MP_L}{MP_k} &= \frac{\Delta k}{\Delta L}
\end{aligned}`
$$
Note: diminishing returns to additional labor units
]
.pull-right[
<img src="data:image/png;base64,#images/mit_5_3.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[Returns to Scale]
- **Constant returns to scale**: long-run average costs are the same as it increases output
- e.g.: doubling inputs => doubling outputs
$$
`\begin{aligned}
q &= f(L, k)\\
q &= f(2L, 2k)\\
q &= 2*f(L, k)\\
f(2L, 2k)&= 2*f(L, k)
\end{aligned}`
$$
- **Increasing returns to scale:**
  - e.g., doubling inputs > doubling outputs
  - firms learn to specialize

- **Decreasing returns to scale:** 
  - e.g., doubling inputs < doubling outputs
  - difficulty of coordination
]
.panel[.panel-name[RTS 2]
.pull-left[
<img src="data:image/png;base64,#images/mit_5_4a.png" width="80%" style="display: block; margin: auto;" />
]
.pull-right[
<img src="data:image/png;base64,#images/mit_5_4b.png" width="80%" style="display: block; margin: auto;" />
]
Can you have a firm with infinite growth? What happens if a firm grows forever?
]
.panel[.panel-name[RTS 3]

Can you have a firm with infinite growth? What happens if a firm grows forever?

- Monopoly--it would take over the economy

- Eventually, we think returns to scale must decrease

- At some point, doubling the inputs makes the firm too unwieldy to manage

- We think in firm's life cycle, returns to scale are probably increasing, then decreasing--but we don't know when that happens
  - e.g. Google, Amazon showing it happens later than we thought
]
.panel[.panel-name[Productivity]
.pull-left[
- Thomas Malthus (1798)
  - Production of food: labor and land
  - Labor is variable (short- and long-run)
  - Land is fixed
  - Marginal product of labor will decrease given fixed land
  - So he predicted cycles of starvation
  
- World population has increased ~1,000% and we are not facing worldwide starvation

- What did he miss?
]
.pull-right[
- `$q = A*f(L, K)$`

*Standard of living* is determined by productivity
- Given our labor: we need more k or A
- Mostly determined by A

**Total factor productivity:** how much does production go up given an amount of capital and labor
]
]

]

---

## Productivity Discussion

.pull-left[
### Timeline
- 1947 to 1973: 2.5% increase per year
  - every year we can buy 2.5% more things without working more or trying harder
  - This is increasing standard of living

- 1973 to 1990s: growth slowed to 1%    
  - We saved less (so k slower)

- 1995 to 2005: 
  - productivity jumped back up to 2.3% (IT boom)

- Productivity slowed after 2005
  - so technology gains were not persistent
    - lots of hypotheses, no consensus yet
]
.pull-right[
### Questions
- What do we do with the extra productivity gains
    - buy stuff
    - work less

- Who benefits?
  - 45-73
    - productivity growth = ~2.5% per year
    - income growth = 2 to 2.5% per year
  - 73-05
    - productivity growth = 1.5-1.6%
    - average income growth: 0.4%
]

---

## Short Run Costs

.panelset[

.panel[.panel-name[Total Costs]
Jill is setting up her pizzaria with 2 pizza ovens. Each pizza oven costs $400 per week, and each worker costs $650 per week. Let's map out her production function and costs.

`$TC = FC + VC$`
.pull-left[
<table class="table table-striped table-hover table-condensed" style="font-size: 20px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Table: Short Run Production and Costs</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> Workers </th>
   <th style="text-align:center;"> Ovens </th>
   <th style="text-align:center;"> Pizzas </th>
   <th style="text-align:center;"> FC </th>
   <th style="text-align:center;"> VC </th>
   <th style="text-align:center;"> TC </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $0 </td>
   <td style="text-align:center;"> $800 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $650 </td>
   <td style="text-align:center;"> $1,450 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 450 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $1,300 </td>
   <td style="text-align:center;"> $2,100 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 550 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $1,950 </td>
   <td style="text-align:center;"> $2,750 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 600 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $2,600 </td>
   <td style="text-align:center;"> $3,400 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 625 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $3,250 </td>
   <td style="text-align:center;"> $4,050 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 640 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $3,900 </td>
   <td style="text-align:center;"> $4,700 </td>
  </tr>
</tbody>
</table>
]
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]
.panel[.panel-name[MC vs. ATC]
.pull-left[
- `$ATC = \frac{TC}{Q}$`
- **marginal cost**
  - change in firm’s TC from producing one more unit of a good or service
  - `$MC = \frac{\Delta TC}{\Delta Q}$`

]
.pull-right[
- Why U-shaped MC and ATC curves
  - Returns to specialization can `$\uparrow$` MP, causing MC to `$\downarrow$`
  - When MC < ATC, ATC `$\downarrow$` and vice versa

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.panel[.panel-name[Costs Table]
.pull-left[
We know that total costs can be divided into fixed and variable costs:
$$
TC = FC + VC
$$
]
.pull-right[

Dividing both sides by output (Q) gives a useful relationship:

$$
`\begin{aligned}
\frac{TC}{Q} &= \frac{FC}{Q} + \frac{VC}{Q}\\
ATC &= AFC + AVC
\end{aligned}`
$$

]

<table class="table table-striped table-hover table-condensed" style="font-size: 16px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Table: Short Run Production and Costs</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> Workers </th>
   <th style="text-align:center;"> Ovens </th>
   <th style="text-align:center;"> Pizzas </th>
   <th style="text-align:center;"> FC </th>
   <th style="text-align:center;"> VC </th>
   <th style="text-align:center;"> TC </th>
   <th style="text-align:center;"> MC </th>
   <th style="text-align:center;"> ATC </th>
   <th style="text-align:center;"> AFC </th>
   <th style="text-align:center;"> AVC </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $0 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> NA </td>
   <td style="text-align:center;"> NA </td>
   <td style="text-align:center;"> NA </td>
   <td style="text-align:center;"> NaN </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $650 </td>
   <td style="text-align:center;"> $1,450 </td>
   <td style="text-align:center;"> $3.25 </td>
   <td style="text-align:center;"> $7.25 </td>
   <td style="text-align:center;"> $4.00 </td>
   <td style="text-align:center;"> $3.25 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 450 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $1,300 </td>
   <td style="text-align:center;"> $2,100 </td>
   <td style="text-align:center;"> $2.60 </td>
   <td style="text-align:center;"> $4.67 </td>
   <td style="text-align:center;"> $1.78 </td>
   <td style="text-align:center;"> $2.89 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 550 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $1,950 </td>
   <td style="text-align:center;"> $2,750 </td>
   <td style="text-align:center;"> $6.50 </td>
   <td style="text-align:center;"> $5.00 </td>
   <td style="text-align:center;"> $1.45 </td>
   <td style="text-align:center;"> $3.55 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 600 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $2,600 </td>
   <td style="text-align:center;"> $3,400 </td>
   <td style="text-align:center;"> $13.00 </td>
   <td style="text-align:center;"> $5.67 </td>
   <td style="text-align:center;"> $1.33 </td>
   <td style="text-align:center;"> $4.33 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 625 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $3,250 </td>
   <td style="text-align:center;"> $4,050 </td>
   <td style="text-align:center;"> $26.00 </td>
   <td style="text-align:center;"> $6.48 </td>
   <td style="text-align:center;"> $1.28 </td>
   <td style="text-align:center;"> $5.20 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 640 </td>
   <td style="text-align:center;"> $800 </td>
   <td style="text-align:center;"> $3,900 </td>
   <td style="text-align:center;"> $4,700 </td>
   <td style="text-align:center;"> $43.33 </td>
   <td style="text-align:center;"> $7.34 </td>
   <td style="text-align:center;"> $1.25 </td>
   <td style="text-align:center;"> $6.09 </td>
  </tr>
</tbody>
</table>
]

.panel[.panel-name[Costs Graph]
.pull-left[
This results in both ATC and AVC having their U-shaped curves.

The MC curve cuts through each at its minimum point, since both ATC and AVC “follow” the MC curve.

Also notice that the vertical sum of the AVC and AFC curves is the ATC curve.

And because AFC gets smaller, the ATC and AVC curves converge.

]
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.panel[.panel-name[Cost Function]
.pull-left[

- Cost function
  - `$TotalCost = \overline{k}*rent + L*wage$`
  - `$C = \overline{k}*r + L*w$`

- Example
  - `$q = \sqrt{L*\overline{k}}$`
  - r = $10
  - w = $5

Rewrite production function in terms of labor
  
$$
`\begin{aligned}
q &= \sqrt{L*\overline{k}}\\
L &= \frac{q^2}{\overline{k}}
\end{aligned}`
$$

]
.pull-right[
Plug into cost function: `$C = 10* \overline{k} + 5*\frac{q^2}{\overline{k}}$`

If fixed capital == 1:

$$
`\begin{aligned}
C &= 10*1 + 5*\frac{q^2}{1}\\
C &= 10 + 5q^2\\
NOTE:TC &= FC + VC
\end{aligned}`
$$

<br>

*Yay! You just derived the short-run cost function!*
]
]
.panel[.panel-name[Cost Curves]
.pull-left[
If fixed capital == 1:
$$
`\begin{aligned}
TC &= 10 + 5q^2\\
MC &= \frac{\Delta TC}{\Delta q}\\
ATC &= \frac{TC}{q}
\end{aligned}`
$$

- Marginal cost: cost to produce the next unit
- Average cost: average cost to produce each unit
  - declining at first--pay off fixed costs
  - increasing later--increasing average variable costs
- e.g. Build a plant
  - Initial cost is high, but then declines
  - As output increases, need to hire more workers => costs go up
- **Marginal cost intersects average total cost at the minimum** 
]
.pull-right[
<img src="data:image/png;base64,#images/mit_6_1.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[MC]
**What's the relationship between marginal cost and marginal product of labor?**

$$
`\begin{aligned}
MC &= \frac{\Delta TC}{\Delta q} = w*\frac{\Delta L}{\Delta q}\\
MP_L &= \frac{\Delta q}{\Delta L}\\
\\
\rightarrow MC &= w * \frac{1}{MP_L}
\end{aligned}`
$$
- the higher the wage, the higher the marginal cost
- the higher the productivity `$(MP_L)$`, the lower the marginal cost
- low productivity workers cost more than high productivity workers
- so we consider wages in conjunction with productivity
]
]

---

## Long Run Costs
.panelset[
.panel[.panel-name[Intro]
**How do we choose the mix of workers and machines to produce a given quantity most efficiently?**

**2 steps**
1. For a given quantity, what's the right mix of capital and labor to minimize the cost of producing that quantity?
2. As we vary the quantity, what's the new right mix of k and L?

We want to find the combination of k and L that minimize costs.
]
.panel[.panel-name[Isocost]
.pull-left[
- Isocost curves 
  - are mappings of `$TC = rk+wL$`
  - show all combinations of two inputs that have the same total cost
- What combinations of k and L cost you $100?
- This graph shows three isocost lines for three different total costs.
- Higher levels of total cost shift the isocost line upward.
- While we only show three isocost lines there is a different isocost line for every level of total cost.
- Have to graph multiples because we don't know which is correct unlike budget constraint
- `$Slope = \frac{\Delta k}{\Delta L} = -\frac{w}{r}$`
]
.pull-right[
<img src="data:image/png;base64,#images/mit_6_2.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[Cost Min]
.pull-left[
- With the same logic as consumer theory, we produce at maximum efficiency at the point of tangency between the isoquant and isocost curves
- Slope of isoquant: `$MRTS =-\frac{MP_L}{MP_k}$`
- Slope of isocost: `$-\frac{w}{r}$`

$$
`\begin{aligned}
MRTS = -\frac{MP_L}{MP_k} &= -\frac{w}{r}\\
\frac{MP_L}{w} &= \frac{MP_k}{r}
\end{aligned}`
$$

- Does the next dollar of wages deliver the same productivity return as the next dollar of machine rental?

]
.pull-right[
<img src="data:image/png;base64,#images/mit_6_3.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[Changes]
.pull-left[
If the technology changes or the prices of the inputs change then the cost-minimizing input choice will change as well.

- `$r$` = $10
- `$w_1$` = $5
- `$w_2$` = $10

- changing price while holding production constant
- so an increase in wages => hire fewer workers, more machines

- Note: it's not like budget constraint where income is fixed

]
.pull-right[
<img src="data:image/png;base64,#images/mit_6_4.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[Expansion Path]
.pull-left[
How do your costs expand as you produce more?

Firms can create a long-run expansion path using isoquant and isocost lines.

This graph shows how a firm might elect to increase output and still produce at the lowest possible cost for a given quantity.

This says you always want the same ratio of workers to machines.

The long-run expansion path => long-run cost curve

For every level of production, this is the optimal combination of k and L
]
.pull-right[
<img src="data:image/png;base64,#images/mit_6_5a.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[Nonlinear Expansion]
.pull-left[
<img src="data:image/png;base64,#images/mit_6_5b.png" width="100%" style="display: block; margin: auto;" />
]
.pull-right[
<img src="data:image/png;base64,#images/mit_6_5c.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[LRAC]
.pull-left[
- Long run costs are always no higher (and generally lower) than short run costs
- Consider a firm with 3 sizes of plants: small `$(SRAC_1)$`, medium `$(SRAC_2)$`, large `$(SRAC_3)$`
- Compare `$SRAC_1$` to `$SRAC_3$`
  - For small quantities of production, 
    - `$SRAC_1$` lies below `$SRAC_3$`
    - At level of `$q_1$`, `$SRAC_3$` is much, much higher than `$SRAC_1$`
  - For large quantities of production,
    - `$SRAC_1$` lies above `$SRAC_3$`
    - At level of `$q_1$`, `$SRAC_1$` is much, much higher than `$SRAC_3$`
- For different levels of production, these give the different optimal short-run cost curves
- Long run, you get to choose your production => LRAC is lower envelope of SRACs
]
.pull-right[
<img src="data:image/png;base64,#images/mit_6_6.png" width="100%" style="display: block; margin: auto;" />
]
]
.panel[.panel-name[RTS]
.pull-left[
**Long-run average costs and returns to scale**

- **Economies of scale**: The firm’s LRACs falling as it increases the quantity of output it produces
  
  
- **Minimum efficient scale**: lowest level of output at which all economies of scale are exhausted
- **Constant returns to scale**: a firm’s LRAC remains unchanged as it increases output
- **Diseconomies of scale**: a firm’s LRACs rise as the firm increases output
  - firm gets too large to manage effectively, 
  - or because the firm has to employ workers or other factors of production that are less well suited to production

]
.pull-right[
<img src="data:image/png;base64,#images/fig_11_6.png" width="100%" style="display: block; margin: auto;" />
]
]

]

---